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Spacelike Singularities and Hidden Symmetries of Gravity
 LIVING REV. REL
, 2008
"... We review the intimate connection between (super)gravity close to a spacelike singularity (the “BKLlimit”) and the theory of Lorentzian KacMoody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing ..."
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We review the intimate connection between (super)gravity close to a spacelike singularity (the “BKLlimit”) and the theory of Lorentzian KacMoody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinitedimensional KacMoody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a selfcontained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinitedimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian KacMoody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of Mtheory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to
KCLMTH0907 Exotic E11 branes as composite gravitational solutions
, 908
"... A twoparameter group element is presented that interpolates between Mbrane solutions. The group element is used to interpret a number of exotic branes related to the generators of the adjoint representation of E11 as nonmarginal halfBPS bound states of Mbranes. It is conjectured that the adjoin ..."
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A twoparameter group element is presented that interpolates between Mbrane solutions. The group element is used to interpret a number of exotic branes related to the generators of the adjoint representation of E11 as nonmarginal halfBPS bound states of Mbranes. It is conjectured that the adjoint representation of E11 contains only generators related to bound states of fundamental Mbranes which, in the limit, may be understood as membrane molecules.
Higher derivative type II string effective actions, automorphic forms and En
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On brane solutions related to nonsingular KacMoody algebras
, 810
"... A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 × M1 ×... × Mn, where Mi are Einstein spaces (i ≥ 1). The sigmamodel approach and exact solutions with intersecting composite branes (e.g. solutions with ..."
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A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 × M1 ×... × Mn, where Mi are Einstein spaces (i ≥ 1). The sigmamodel approach and exact solutions with intersecting composite branes (e.g. solutions with harmonic functions, Sbranes and black branes) with intersection rules related to nonsingular KacMoody (KM) algebras (e.g. hyperbolic algebras) are reviewed. Some examples of solutions, e.g. corresponding to hyperbolic KM algebras: H2(q, q), AE3, HA (1) 2 KM algebra P10, are presented.
Hidden Symmetry Unmasked: Matrix Theory and E11=E (3)
, 2004
"... Dimensional reduction of elevendimensional supergravity to zero spacetime dimensions is expected to give a theory characterized by the hidden symmetry algebra E11, the endpoint of the CremmerJulia prediction for the sequence of dimensional reductions of 11d supergravity to spacetime dimensions. I ..."
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Dimensional reduction of elevendimensional supergravity to zero spacetime dimensions is expected to give a theory characterized by the hidden symmetry algebra E11, the endpoint of the CremmerJulia prediction for the sequence of dimensional reductions of 11d supergravity to spacetime dimensions. In recent work, we have given a prescription for the spacetime reduction of a supergravityYangMills Lagrangian with large N flavor symmetry such that the local symmetries of the continuum Lagrangian are preserved in the resulting reduced matrix Lagrangian. This new class of reduced matrix models are the basis for a nonperturbative proposal for M theory we have described in hepth/0408057. The matrix models are also characterized by hidden symmetry algebras in precise analogy with the CremmerJulia framework. The rank eleven algebra E11=E (3) 8 is also known as the veryextension of the finitedimensional Lie algebra E8. In an independent stream of work (hepth/0402140), Peter West has provided evidence which supports the conjecture that M theory has the symmetry algebra E11, showing that it successfully incorporates both the 11d supergravity limit, as well as the 10d type IIA and type IIB supergravities, and inclusive of the full spectrum of NeveuSchwarz and Dirichlet pbranes. In this topical review, we give a pedagogical account of these recent developments also providing an assessment of the insights that might be gained from linking the algebraic and reduced matrix model perspectives in the search for M theory. Necessary mathematical details are covered starting from the basics in the appendices. 1
ElectricMagnetic Duality and the Brane Spectrum of M Theory
, 2004
"... Poincare duality in ten dimensions implies the existence of a scalar field strength, the magnetic dual of the tenform field strength of the massive type IIA string theory. In this paper we summarize the evidence for the existence of point sources of the associated Dirichlet (2)brane charge, from f ..."
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Poincare duality in ten dimensions implies the existence of a scalar field strength, the magnetic dual of the tenform field strength of the massive type IIA string theory. In this paper we summarize the evidence for the existence of point sources of the associated Dirichlet (2)brane charge, from four independent perspectives: (i) the massive IIA supergravity Lagrangian and algebraic jade relations for the spectrum of pbrane tensions, (ii) a soliton solution of the massive IIA supergravity, and of M theory, exhibiting a point source of magnetic D(2)brane charge, (iii) analysis of the global symmetry algebra of the massive type IIA supergravity theory, and, (iv) the worldsheet computation of the tension of a D(2)brane in type I ′ string theory with boundary state description. We point out that the concrete worldsheet evidence for a Dpbrane spectrum with precisely twelve elements, −2 ≤ p ≤ 9, in the type II string theories can be understood as a simple consequence of Poincare duality for the associated field strengths in eleven dimensions. Further, since the (1)form potential is simply the generator of spacetime translations in any dimension, we find, remarkably, that the full spectrum of Dirichlet pform potentials in higher dimensions, 0 ≤ d ≤ 11, can be inferred by the dimensional uplifting of a In this paper, we will assemble the evidence from four independent perspectives for the existence of point sources carrying Dirichlet (2)brane charge in String/M theory. The individual pieces of